Zhang [1]} and Lutwak et al. [2]} formulated
and proved a remarkable affine \(L_p\)  Pólya-Szegö principle for \(1\le p<n\) , which significantly strengthens the classical Pólya-Szegö principle. Later, Cianchi et al. [3]} perfectly completed the picture of affine Pólya-Szegö principle (for general \(p\ge 1\) ). In [4]}, Haberl, Schuster and Xiao obtained a beautiful asymmetric version of the affine Pólya-Szegö principle and proved that it is stronger and directly implies the symmetric form of Cianchi et al.
